Rewrite as a simplified fraction. ${0.9\overline{98} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 998.9898...\\ 10x &= 9.9898...\end{align*}}$ Subtracting the two equations, we have: ${990x = 989}$ ${x = \dfrac{989}{990}} $